CU, Incorporated (CUI) produces copper contacts that it uses in switches and relays. CUI needs to determine the order quantity, Q, to meet the annual demand at the lowest cost. The price of copper depends on the quantity ordered. Here are price-break and other data for the problem:

Price of copper $ 0.82 per pound up to 2,499 pounds

$ 0.81 per pound for orders between 2,500 and 5,000 pounds

$ 0.80 per pound for orders greater than 5,000 pounds

Annual demand 50,000 pounds per year

Holding cost 20 percent per unit per year of the price of the copper

Ordering cost $ 30

Which quantity should be ordered?

If CUI buys at $0.82 per pound

Annual demand (Co) = 50,000 pounds

Ordering cost per order (Co) = $30

Holding cost per item per annum (H) = 20% x $0.82 = $0.164

EOQ = √2DCo

H

EOQ = √2 x 50,000 x $30

$0.164

EOQ = 4,277 units

The solution is not feasible since 4,277 units could not be bought at $0.82 per pound.

If CUI buys at $0.81 per pound

Annual demand (Co) = 50,000 pounds

Ordering cost per order (Co) = $30

Holding cost per item per annum (H) = 20% x $0.81 = $0.162

EOQ = √2DCo

H

EOQ = √2 x 50,000 x $30

$0.162

EOQ = 4,303 units

Total cost for 4,303 units

= DCo + QH + P x D

Q 2

= 50,000 x $30 + 4,303 x $0.162 + $0.81 x 50,000

4,303 2

= $348.59 + $348.54 + $40,500

= $41,197.13

If CUI buys at $0.80 per pound

Annual demand (Co) = 50,000 pounds

Ordering cost per order (Co) = $30

Holding cost per item per annum (H) = 20% x $0.80 = $0.16

EOQ = √2DCo

H

EOQ = √2 x 50,000 x $30

$0.16

EOQ = 4,330 units

The solution is not feasible since 4,330 units could not be bought at $0.80 per pound. Thus, EOQ is 5,001 units.

Total cost for 5,001 units

= DCo + QH + P x D

Q 2

= 50,000 x $30 + 5,001 x $0.16 + $0.80 x 50,000

5,001 2

= $299.94 + $400.08 + $40,000

= $40,700.02

Thus, EOQ equals 5,001 units because the quantity minimises the total cost.

Explanation:

EOQ is a function of square root of 2 multiplied by annual demand and ordering cost per order divided by holding cost per item per annum.

Since this question involves discounts, there is need to calculate EOQ at various discount levels. Holding cost is a function of price. For instance, when price is $0.82, holding cost is 20% of $0.82.

We will calculate the EOQ at various prices and corresponding total cost. Finally, we will consider the quantity that minimizes the total cost. Thus, EOQ equals 5,001 units.